Macaulay Duration Overview, How To Calculate, Factors

These organizations often hold bonds in their fixed-income portfolios with prices that can fluctuate based on interest rate changes. In asset-liability portfolio management, duration-matching is a method of interest rate immunization. A change in the interest rate affects the present value of cash flows, and thus affects the value of a fixed-income portfolio. Modified duration is important because it allows us to assess the risk of investing in bonds. If you’re investing in bonds, you want to know how much the bond’s price will fluctuate in response to changes in interest rates. Modified duration gives you a sense of the bond’s price sensitivity, which can help you make a more informed investment decision.

Modified duration follows the concept that interest rates and bond prices move in opposite directions. This formula is used to determine the effect that a 100-basis-point (1%) change in interest rates will have on the price of a bond. Modified duration is not a perfect measure of interest rate risk.

1. It calculates the weighted average time until a bond’s cash flows are received, including all coupon payments and the return of principal at maturity.
2. In general, bond prices rise when interest rates fall and vice versa.
3. Next, the value is calculated for each period and added together.
4. The content is current as of the time of writing or as designated within the material.
5. This resulting percentage change in the bond, for an interest rate increase from 8% to 9%, is calculated to be -2.71%.
6. While yes, understanding a bond’s face value, its duration, and its coupon rate (or interest rate) is easy, other things about a bond can be much more complex.

Calculating Modified Duration from Prices

This bond has an annual coupon rate (the yield paid through maturity) of 5%. Modified duration can be calculated by dividing the Macaulay duration of the bond by 1 plus the periodic interest rate, which means a bond’s Modified duration is generally lower than its Macaulay duration. If a bond is continuously compounded, the Modified duration of the bond equals the Macaulay duration.

A fixed income security with a greater duration indicates a higher sensitivity to interest rates and thus, the greater the interest rate risk it has. And as the price of most fixed income securities have an inverse relationship with yields, a security with a greater duration will have more interest rate risk than a security with a shorter duration. With the inequalities being strict unless it has a single cash flow. In terms of standard bonds (for which cash flows are fixed and positive), this means the Macaulay duration will equal the bond maturity only for a zero-coupon bond. The Macaulay duration is the sum of these weighted-average time periods, which is 1.915 years. An investor must hold the bond for 1.915 years for the present value of cash flows received to exactly offset the price paid.

1. In contrast, the modified duration identifies how much the duration changes for each percentage change in the yield while measuring how much a change in the interest rates impacts the price of a bond.
2. The face value is the principal amount that you’ll receive at the maturity of the bonds.
3. For example, the annuity above has a Macaulay duration of 4.8 years, and we might think that it is sensitive to the 5-year yield.
4. In summary, Modified and Macaulay Durations are valuable tools in analyzing fixed-income securities, but they do have limitations.
5. While modified duration and Macaulay duration may seem similar at first glance, they take different approaches to measuring a bond’s price sensitivity to changes in interest rates.

Example of Macaulay Duration

Sometimes we can be misled into thinking that it measures which part of the yield curve the instrument is sensitive to. After all, the modified duration (% change in price) is almost the same number as the Macaulay duration (a kind of weighted average years to maturity). what is modified duration For example, the annuity above has a Macaulay duration of 4.8 years, and we might think that it is sensitive to the 5-year yield.

When the commodity is money, spot prices are called spot rates (a.k.a., spot interest rate). A spot price is simply the market’s current price to buy or sell a commodity for immediate delivery… For example, if an investor owns a bond with a Macaulay Duration of 5 years, it means that if interest rates rise by 1%, the bond’s price will fall by approximately 5%.

Effective Duration

Modified duration can help investors and portfolio managers make more informed decisions about bond investments. For example, if an investor expects interest rates to rise, they may consider investing in bonds with shorter modified durations to reduce their exposure to interest rate risk. Both modified and dollar duration, therefore, are metrics for how sensitive a bond’s price is to movements in its yield. The price of a longer modified or dollar duration fixed-income instrument will move more significantly to a change in yield as compared to the price of a shorter modified or dollar duration instrument. The modified duration measure takes duration one step further and gives the percentage change in the bond’s price per basis point.

Dollar duration or DV01 is the change in price in dollars, not in percentage. It gives the dollar variation in a bond’s value per unit change in the yield. It is often measured per 1 basis point – DV01 is short for “dollar value of an 01” (or 1 basis point). The name BPV (basis point value) or Bloomberg “Risk” is also used, often applied to the dollar change for a $100 notional for 100bp change in yields – giving the same units as duration. PV01 (present value of an 01) is sometimes used, although PV01 more accurately refers to the value of a one dollar or one basis point annuity.

Modified duration takes into account the fact that as interest rates change, the expected cash flows from the bond may also change. This measure measures the percentage change in bond price for a 1% change in yield, assuming all other factors remain constant. On the other hand, Macaulay duration measures the weighted average time to receive all the bond’s cash flows, taking into account the present value of each cash flow and the bond’s maturity. Modified duration measures the size of the interest rate sensitivity.

Dollar duration measures the dollar change in a bond’s value to a change in the market interest rate, providing a straightforward dollar-amount computation given a 1% change in rates. A bond’s price is calculated by multiplying the cash flow by 1, minus 1, divided by 1, plus the yield to maturity, raised to the number of periods divided by the required yield. The resulting value is added to the par value, or maturity value, of the bond divided by 1, plus the yield to maturity raised to the total number of periods. Modified duration helps investors understand this relationship by measuring the sensitivity of a bond’s price to changes in interest rates.

Dollar Duration (“Risk”)

For example, if a bond has a modified duration of 5, it means that for every 1% increase in interest rates, the bond’s price will decrease by 5%. Macaulay Duration is a financial concept that is used to measure the sensitivity of a bond’s price to interest rate changes. It is named after Frederick Macaulay, who introduced the concept in 1938.